To find the area that would be identified on the shoebox's net, we need to calculate the surface area of the shoebox. A shoebox is a rectangular prism, and the surface area can be calculated using the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where:
- \( l \) = length (104 cm)
- \( w \) = width (72.5 cm)
- \( h \) = height (47.5 cm)
Let's calculate:
- \( lw = 104 \times 72.5 = 7,540 , \text{cm}^2 \)
- \( lh = 104 \times 47.5 = 4,930 , \text{cm}^2 \)
- \( wh = 72.5 \times 47.5 = 3,447.5 , \text{cm}^2 \)
Now, add these areas together:
\[ lw + lh + wh = 7,540 + 4,930 + 3,447.5 = 15,917.5 , \text{cm}^2 \]
Now, multiply this sum by 2 to find the total surface area:
\[ \text{Surface Area} = 2 \times 15,917.5 = 31,835 , \text{cm}^2 \]
It seems there was a small error in the calculation of individual areas, let's double check:
- \( lw = 104 \times 72.5 = 7,540 , \text{cm}^2 \) (Correct)
- \( lh = 104 \times 47.5 = 4,930 , \text{cm}^2 \) (Correct)
- \( wh = 72.5 \times 47.5 = 3,447.5 , \text{cm}^2 \) (Correct)
So, the total surface area calculation is indeed:
\[ \text{Surface Area} = 2(7,540 + 4,930 + 3,447.5) = 2 \times 15,917.5 = 31,835 , \text{cm}^2 \]
Thus, the closest answer from your options is:
31,847.5 cm²
So the correct response is 31,847.5 cm².